meditation on a 1-string chord

> From: <BVAL@IIL.INTEL.COM>
> To: <crazy_music@yahoogroups.com>
> Sent: Friday, July 27, 2001 10:44 AM
> Subject: [cm] Re: pitch adjustment, integer detectors, etc.
>

>
> yes, a kindergartener would say "the overtone series". Then you pick up
> a guitar and play a C13 chord, and compare it to 4-5-6-7-9-11-13 and
> say, "well geee, thats not really it at all". I was dissappointed to
> see the book 'Lies my music teacher taught me' making these sorts of
> claims.

This points out the wonderful variety of perspectives in the different
kinds of analyses of tuning and other aspects of music. Everyone
hears differently, and so while there may be large areas of agreement
among many people about the validity of certain theoretical ideas
about tuning and music, ultimately everyone's perspective on this
is uniquely his/her own.

Please indulge me, and allow me to recount a pleasant experience
I had today ...

I had a rather light schedule today, and while I tuned a small
Wurlitzer upright piano this morning in 12-EDO, and searched
(by ear) for just the right amount of stretch, to even out the
overtone-beating on the low strings, I spent a little while
meditating on the sound of the harmonics of the "C" 2 8ves
below middle-C.

This piano is in pretty good condition (altho I hadn't been
tuned in many years), and as the sound of that string lingered
on and on, it changed slightly, the lower harmonics softening
as the higher harmonics gradually came into better focus.

[refer to mclaren's crazy_music post of a couple of days ago
< note the sloppy scholarship :) >
comparing perception of harmonic ideas while composing,
to looking thru a telescope]

I could clearly hear a beautiful chord... reminiscent of
some of La Monte Young's mellower pieces. I'd describe
the chord like this:

~harmonic 72edo 8ve + cents

14 Bb< 3 967&2/3
11 F^ 3 550
7 Bb< 2 967&2/3
5 E- 2 383&1/3
3 G 1 700
1 C 0 0

[Here's the Monzo 72-EDO notation legend:

symbol 72edo cents

^ +3 50 A
> +2 33&1/3 |
+ +1 16&2/3 plus cents from 12-EDO
0 0
- -1 16&2/3 minus cents from 12-EDO
< -2 33&1/3 |
v -3 50 V ]

Note that I'm thinking (in my mind) in terms
of two different theories, and also with a
variation of the latter one:

1)
the theory of prime-affect, in which the
chord-identites each display a "ness" (in this
case, "2-ness, 3-ness, 5-ness, 7-ness, 11-ness"),
which is primarily a harmonic sensibility.

This is represented by the low-integer proportion.

2)
the equally-divided-pitch-continuum theory, (which
in this case is 72-EDO [= 12 x 6 equal divisions of
the 8ve], or in another description, 72-ED2 [= 12 x 6
equal divisions of the proportion "2"]), which is
primarily a melodic sensibility.

This is represented by the 72-EDO adaptation of
regular meantone-based 12-EDO notation, which
in turn represents specific cents values [12 x 100 =
1200-EDO, which is a finer division in the same genre
of tuning].

All these ideas were turning around in my mind,
as I listened to the 1-string chord resonate,
and I tried to formulate a systematic way of
comprehending in my mind what I was hearing.

It got me to thinking about Schoenberg's compostions
and theories, for reasons which will unfold as I
go along...

A big part of the reason why I value Schoenberg's theories
so much, regardless of scientific experiments which invalidate
them, is because his many of his descriptions resonate so
strongly with my own perceptions.

I'm speculating, but I really strongly suspect that
Schoenberg got many of his harmonic ideas c. 1907-10
from listening to low piano strings as I was doing
today. His _Harmonielehre_ makes references to the
kinds of ideas I presented above, and...

On the Wurlitzer, the "C" another 8ve below that one
bloomed an even richer sonic palette, which reminded
me of Schoenberg's description (in _Harmonielehre_)
of a sustained chord he used in _Erwartung_ which
contains many "dissonant" notes, and, in part, compares
it to the type of "natural" sound like the one I heard.

(Schoenberg also gives another type of analysis which
resembles the theory of "non-harmonic tones" and their
resolution. Martin Vogel has done a JI-based analysis of
this chord, which appeared in abbreviated form in English
in _On the Relations of Tone_, and more fully in German
in _Sch�nberg und die Folgen_, and I have done a more
detailed and extensive one in my book _JustMusic_.)

Anyway, on this lower "C" I could eventually (actually
after quite a long time) hear the 13th harmonic very
clearly, while the 11th died away much faster.

Indeed, as I listened to this lower note I could not
escape the memory of all manner of harmonic snippets
from Schoenberg's compositions of this period, and
especially that big chord from _Erwartung_, which
Schoenberg notes is to be played softly, which really
causes it to resemble the kinds of sounds with which
the Wurlitzer massaged my ears this morning.

So in many ways I was thinking of a very wide variety
of perspectives on tuning theory as I meditated on those
gorgeous 1-note chords. Brian has described Schoenberg's
music as "brutal" and other such ugly epithets, and he's
certainly not alone in that. But Schoenberg's compositions
do have sensously beautiful moments like this one in
_Erwartung_ that are probably the ultimate in abstract
music-making: simply playing around with sounds.

I view Schoenberg's theoretical work as a necessarily vague
exploration of the approximations 12-EDO may make to a vast
multitude of different systematic ways of comprehending
a partitioning of the pitch-continuum. I say necessarily,
because Schoenberg realized that the breadth of these ideas
exceeded not only his own limited mathematical understanding,
but ultimately that of anyone's.

Which leads me back to my opening statement... and which
hopefully will help to explain some of my admiration for
Schoenberg's work.

love / peace / harmony ...

-monz
http://www.monz.org
"All roads lead to n^0"

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--- In tuning@y..., "monz" <joemonz@y...> wrote:

> Note that I'm thinking (in my mind) in terms
> of two different theories, and also with a
> variation of the latter one:
>
> 1)
> the theory of prime-affect, in which the
> chord-identites each display a "ness" (in this
> case, "2-ness, 3-ness, 5-ness, 7-ness, 11-ness"),
> which is primarily a harmonic sensibility.
> This is represented by the low-integer proportion.
>
> 2)
> the equally-divided-pitch-continuum theory, (which
> in this case is 72-EDO [= 12 x 6 equal divisions of
> the 8ve], or in another description, 72-ED2 [= 12 x 6
> equal divisions of the proportion "2"]), which is
> primarily a melodic sensibility.
> This is represented by the 72-EDO adaptation of
> regular meantone-based 12-EDO notation, which
> in turn represents specific cents values [12 x 100 =
> 1200-EDO, which is a finer division in the same genre
> of tuning].
>
> All these ideas were turning around in my mind,
> as I listened to the 1-string chord resonate,
> and I tried to formulate a systematic way of
> comprehending in my mind what I was hearing.

Monz,

Without attempting to take your thoughts quoted here
(which only represent a excerpt from your interesting post),
I had a thought about your dichotomy of "harmonic/melodic"
sensibility, as you put it.

While the dichotomy itself is (I think) a worthwhile one,
perhaps Nature slyly inverts these two aspects. Consider
a keyboard (for computational convenience) with a bass-note
fundamental pitch of 1 Hz (cycle per second), 72 keys per
octave, and plenty of keys to span higher octaves, as well:

(1) Here I see that the trend of greater and greater sub-
divisions of the octave ultimately tends toward a limit
where, for instance, on the keyboard described above,
there exists an individual key for *each and every*
possible harmonic, or "partial", of the 1 Hz bass-note.
Thus, the sound spectrum approaches one that could *also*
be characterized as exclusively "harmonic", where,
relative to the 1 Hz "tonic", ALL of its natural harmonics are
represented, and ALL of the harmonics of any of the keys
also represent integer multiples of that 1 Hz fundamental.

(2) In my "harmonic dual" theory, where, in the case of the
Ellis' 12-tone "Duodene" JI scale, the overlapping of the
harmonics of simultaneously sounded dyadic tone pairs
of the low numbered 5-limit prime interval ratios which
are contained within the "Duodene" result in patterns
of "movement" (counted by the movement in *keys*)
which result in distinct and symmetrical locations on
the keyboard where the *harmonics* which are
generated by any two tones within the (in this case,
12-tone scale) will overlap, and in that manner
likely (in some way) affect the sense of "cordance".
Here, the specific values of the exponents of the prime
factors of the scale intervals, in a systematic form
(as you and I have discussed in our recent private
communications) clearly influence the form of the
pattern of *keys* between which "consonant" dyads
may be formed on the (12-tone, in this case) keyboard,
which, in turn, reflects a characteristic of interacting
*harmonics* (between the various 12 interval ratios of
Ellis' "Harmonic Duodene" scale, and, perhaps also,
for certain other similarly structured N-tone scales).
Here, then is a case where the "2-ness, 3-ness,
5-ness, and perhaps, also, the 7-ness, 11-ness, etc.
clearly comes into play, not necessarily in the sense
of separable "prime-voices", but, instead in the sense
of demonstrable "intertwining" (for lack of a better term)
in the course of the occurance of often perceived
"harmony" between the two tones of a dyad, these
patterns (or "structures") of movement in *keys* to
realize "harmonious" combinations existing in what
are symmetrical patterns around the "harmonic duals"
(1/1 and 3/2, 9/8 and 4/3, 6/5 and 5/4, 8/5 and 15/8,
16/15 and 45/32).

To summarize my thoughts here, perhaps a continuum
exists between a "small numbered" scale (such as the
12-note "Harmonic Duodene"), where the primes, which
predominately exist in what are "low-numbered" interval
ratios, govern - at what particular *keys* - the *harmonics*
will (in coinciding, or overlapping) interact to generate a
"consonance" (due to low numbered "inter-tone" ratios),
while a "large numbered" scale (such as 72-note EDO)
is, itself, virtually a keyboard of individually selectable
*harmonics* (of the 1 Hz bass-tone fundamental, and
to an increasing extent as the number of scale intervals
per octave is increased, of the various integer multiples
of the 1 Hz fundamental, as well), which are selected by
striking various *keys* located on the keyboard.

Once again, in scales with a small number of interval
ratios (such as the 12-tone Duodene), the *harmonic*
structure dictates which *keys* may be successfully
played simultaneously (without suffering ear-pains)
in specific patterns above/below the *keys* which
represent the "harmonic duals" described above,

while in scales with a large number of intervals within
the octave (such as 72-note EDO), the *key* structure
dictates which *harmonics* may be played simultan-
eously in specific patterns above/below whatever may
be the chosen *key* representing a reference "tonic".

Thus, duality upon duality exists in this world within a world...

Respectfully, J Gill

--- In tuning@y..., "monz" <joemonz@y...> wrote:

/tuning/topicId_26516.html#26516

Hi Monz...

Ever wonder why the piano tuner who banged on the lowest note of the
piano for over an hour was never hired back again??

(just kidding...)

________ _______ ________
Joseph Pehrson